On Yokoi's Invariants and the Ankeny-Artin-Chowla conjecture

Işlkay S., Peki˙n A.

International Journal of Number Theory, cilt.18, sa.3, ss.473-484, 2022 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 18 Sayı: 3
  • Basım Tarihi: 2022
  • Doi Numarası: 10.1142/s1793042122500270
  • Dergi Adı: International Journal of Number Theory
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH
  • Sayfa Sayıları: ss.473-484
  • Anahtar Kelimeler: Continued fraction, class number, fundamental unit, real quadratic field, CLASS-NUMBERS, FUNDAMENTAL UNITS, BOUNDS
  • Kocaeli Üniversitesi Adresli: Hayır

Özet

© 2022 World Scientific Publishing Company.Let d be a positive square-free integer and d = (Td + Udd)/2 > 1 be the fundamental unit of the real quadratic field ℚ(d). The Ankeny-Artin-Chowla (AAC) conjecture asserts that Up≢0 (mod p) for primes p 1 (mod 4), which still remains unsolved. In this paper, sufficient conditions for Ud < d have been given in terms of Yokoi's invariants nd and md, and it has been shown that the AAC conjecture is true in some special cases.